The Investigative Committee, which probes major crimes, said its North Caucasus regional branch had detained a 21-year-old local man over last week's attack, in which six soldiers and six rebels died.
"One of the attackers has been detained -- a resident of Chechnya's Naursky district, Ibragim Dzhamalov," it said, adding that "he gave testimony admitting guilt."
The Islamic State group claimed responsibility for the March 24 attack, which targeted a base of Russia's National Guard, a new branch of troops which answers directly to President Vladimir Putin and is tasked with defending borders and counter extremism.
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On Saturday, the Investigative Committee referred to the attackers as "members of an illegal armed band," saying they had guns and knives.
It said six soldiers were killed and three wounded in the strike, while six assailants were killed by answering fire.
Chechnya was the scene of two separatist wars in the 1990s and early 2000s, but violence in the region has largely been suppressed under the iron-fisted rule of strongman leader Ramzan Kadyrov.
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Kadyrov responded to the IS claim by promising to wage a "ferocious fight" against the militants.
"These demons have treacherous intentions: as we have seen they do not want to stop," he said, quoted by the Interfax news agency.
The Russian North Caucasus has been one of the major sources of foreign militants fighting in Syria and Iraq.
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